Sean O'Rourke

Nick Lorenzo, Sean O'Rourke, Theresa Scarnati

In order to encode additional statistical information in data fusion and transfer learning applications, we introduce a generalized covariance constraint for the matching component analysis (MCA) transfer learning technique. We provide a closed-form solution to the resulting covariance-generalized optimization problem and an algorithm for its computation. We call the resulting technique -- applicable to both data fusion and transfer learning -- covariance-generalized MCA (CGMCA). We also demonstrate via numerical experiments that CGMCA is capable of meaningfully encoding into its maps more information than MCA.

Sean O'Rourke, Van Vu, Ke Wang

The Davis-Kahan-Wedin $\sin Θ$ theorem describes how the singular subspaces of a matrix change when subjected to a small perturbation. This classic result is sharp in the worst case scenario. In this paper, we prove a stochastic version of the Davis-Kahan-Wedin $\sin Θ$ theorem when the perturbation is a Gaussian random matrix. Under certain structural assumptions, we obtain an optimal bound that significantly improves upon the classic Davis-Kahan-Wedin $\sin Θ$ theorem. One of our key tools is a new perturbation bound for the singular values, which may be of independent interest.